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NEETPhysicsCurrent Electricity

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): When two electric bulbs of 40 W and 100 W (both designed for 220 V ) are connected in series across a 220 V supply, the 40 W bulb dissipates more power than the 100 W bulb. Reason (R): In a series circuit, the current remains the same and power dissipated is directly proportional to the resistance,

Options

  1. ABoth (A) and (R) are true and (R) is the correct explanation of (A)
  2. BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
  3. C(A) is true but (R) is false
  4. D(A) is false but (R) is true

Correct answer

A. Both (A) and (R) are true and (R) is the correct explanation of (A)

Step-by-step solution

The resistance of a bulb is given by R = V_ rated ^2 P_ rated . For the 40 W bulb: R₄₀ = (220)^2 40 . For the 100 W bulb: R₁₀₀ = (220)^2 100 . Since 40 R₁₀₀ . The 40 W bulb has a higher resistance. When connected in series, the same current I flows through both bulbs. The actual power dissipated in the circuit is P = I^2 R . Since R₄₀ > R₁₀₀ , the power dissipated by the 40 W bulb is greater than that by the 100 W bulb ( P₄₀ > P₁₀₀ ). Therefore, both Assertion (A) and Reason (R) are true, and (R) is the correct exp

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